Graduate Thesis Or Dissertation
 

Estimating population totals from area frame samples

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  • Area frame sampling for agricultural statistics is a procedure currently used by the Statistical Reporting Service of the US Department of Agriculture as well as by agriculture departments in other countries. A primary advantage of the area frame is that it provides complete coverage of the population. In area frame sampling the total area is divided into segments of land that form the sampling units. These segments are delineated by the use of detailed maps and aerial photography. The reporting units, however, are not the segments but are the farms. Since there will be many cases where farms overlap the boundaries of the segments, there have to be rules for assigning data from the farms to the sample segments. Previously used procedures for making this assignment are the open segment method, where the total farm value is assigned to the segment that contains the farm headquarters, the closed segment method, where the actual value associated with the tracts of land contained within the segment is used, and the weighted segment method, where the total farm value is weighted by the proportion of the farm area that is contained in the segment. In this thesis, a general linear unbiased estimator is formulated that includes all previously used methods as special cases. These methods are compared in terms of variance and cost. The optimal estimator depends on the amount and type of overlap of farms with segment boundaries, so it is not possible to give an estimator that is always to be preferred. However, comparisons are made under some special assumptions that, while not particularly realistic, do give insight into conditions affecting the methods and show that the multiplicity rule is an important method to consider.
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